Question: Simplify the following expression: $\dfrac{27r^5}{21r^3}$ You can assume $r \neq 0$.
Explanation: $ \dfrac{27r^5}{21r^3} = \dfrac{27}{21} \cdot \dfrac{r^5}{r^3} $ To simplify $\frac{27}{21}$ , find the greatest common factor (GCD) of $27$ and $21$ $27 = 3 \cdot 3 \cdot 3$ $21 = 3 \cdot 7$ $ \mbox{GCD}(27, 21) = 3 $ $ \dfrac{27}{21} \cdot \dfrac{r^5}{r^3} = \dfrac{3 \cdot 9}{3 \cdot 7} \cdot \dfrac{r^5}{r^3} $ $\phantom{ \dfrac{27}{21} \cdot \dfrac{5}{3}} = \dfrac{9}{7} \cdot \dfrac{r^5}{r^3} $ $ \dfrac{r^5}{r^3} = \dfrac{r \cdot r \cdot r \cdot r \cdot r}{r \cdot r \cdot r} = r^2 $ $ \dfrac{9}{7} \cdot r^2 = \dfrac{9r^2}{7} $